Question: Simplify the following expression: $n = \dfrac{x^2 - 4x - 32}{x - 8} $
First factor the polynomial in the numerator. $ x^2 - 4x - 32 = (x - 8)(x + 4) $ So we can rewrite the expression as: $n = \dfrac{(x - 8)(x + 4)}{x - 8} $ We can divide the numerator and denominator by $(x - 8)$ on condition that $x \neq 8$ Therefore $n = x + 4; x \neq 8$